Find the Degree, Leading Term, and Leading Coefficient f(x)=-2x^2-4x^6-3x^3-8

$f (x) = - 2 x^{2} - 4 x^{6} - 3 x^{3} - 8$

Step 1

Move $- 2 x^{2}$ .

$f (x) = - 4 x^{6} - 3 x^{3} - 2 x^{2} - 8$

Step 2

The degree of a polynomial is the highest degree of its terms.

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$- 4 x^{6} \to 6$

$- 3 x^{3} \to 3$

$- 2 x^{2} \to 2$

$- 8 \to 0$

The largest exponent is the degree of the polynomial.

$6$

Step 3

The leading term in a polynomial is the term with the highest degree.

$- 4 x^{6}$

Step 4

The leading coefficient of a polynomial is the coefficient of the leading term.

The leading term in a polynomial is the term with the highest degree.

$- 4 x^{6}$

The leading coefficient in a polynomial is the coefficient of the leading term.

$- 4$

Step 5

List the results.

Polynomial Degree: $6$

Leading Term: $- 4 x^{6}$

Leading Coefficient: $- 4$